The mathematical and computer modelling of microwave semiconductor devices

The equations governing the modelling of several microwave semiconductor devices are described, with particular attention being paid to the simulation of high speed microwave MESFET and HEMT devices. The MESFET is modelled using the “hydrodynamic equations” consisting of the coupled Poisson, current continuity, and energy transport equations. In order to obtain positive numerical diffusion over all the ranges of the physical parameters, it is found and reported here for the first time that interpolation of the electron temperature between grid points must be done using a logarithmic mean which lies between the corresponding arithmetic and geometric means. In the HEMT simulation, the above equations are augmented by the Schrödinger equation which must be solved self-consistently for the electron energy sub-bands. Simulation results are presented for the above devices, with a multigrid method applied to the HEMT device.